Excess headspace absolutely can cause flattened primers. I once experienced a complete head separation on a .22-250 Rem case because of it, and once is enough!
What happens during the milliseconds of the firing sequence is the firing pin pushes the case forward in the chamber until the shoulder contacts the front of the chamber. At this point, the case head is unsupported due to perhaps a few thousandths of an inch of excess headspace. The firing pin continues to drive forward detonating the primer. The charge ignites and rapidly reaches peak pressure. The brass expands and grips the chamber walls. The unsupported head is slammed back to the breech face (or bolt face), causing the brass to stretch where it becomes thinner just in front of the case web. (if headspace is really excessive, this can often be seen or measured if you section a case lengthwise). With old tarnished brass, you might also see a bright stretch ring after firing, just in front of the web. At the same time, the thin primer cup bulges out or begins to back out of the case. Then it is also slammed under full chamber pressure into the breech or bolt face, causing it to flatten.
This primer flattening can be severe even with loads that are well below an excessive maximum pressure. In the case of the two cartridges I fired just before the head separation, it would have been difficult to see where the primer edge ended, and the case began, except that the CCI primers were silver instead of brass. Extraction in a VZ-24 98 Mauser action was also difficult. Foolishly, I decided to try one more, and that was the cartridge that had the complete head separation. It felt like being violently being punched in both eyes, and I was totally blinded for roughly half an hour, until my vision slowly came back. For once, I had the range to myself, so there was no one to help me. A lot of shit goes through your mind when you are blinded. The wetness I felt on my face was blood, thankfully. At first I thought it was eyeball juice.
I had a strange vee shaped pattern of powder burns and brass particles surrounding my right eye. I learned a couple years later that Paul Mauser redesigned the 98 Mauser bolt shroud to deflect gasses from a ruptured cartridge between the shooter's eyes in that vee shaped pattern, and can attest that it worked... but I would not want to try it again.
I would suggest trying to find a gunsmith who has .222 Rem headspace gauges. You might have a chamber that is on the long side, but still in tolerance. So the factory load length brass could exhibit this symptom to a degree, since it must be sized to fit any factory chamber. In my case, I was given a set of dies and several boxes of brass that had been reloaded multiple times without annealing. I set the dies up to contact the shoulder of the old fired brass, which had apparently been used in a rifle with a minimum headspace chamber. Being work hardened, it was more prone to a separation, rather than simply stretching. When I later tried the exact same load using new unfired brass, I had no primer flattening to speak of, and extraction was easy. Of course, I tested the gun with the new brass by tying it to an old tire, and pulling the trigger with a long string, while standing behind a large oak tree.
Excess headspace can be due to a chamber that is longer than SAAMI tolerance, but it can also be created by setting up sizing dies incorrectly, and setting the shoulder back. So I would also suggest that you neck size only, or set full length sizing dies to barely kiss the shoulder of your fired brass. Your fired primers are nowhere near as flattened as mine were. I think the strange look of your firing pin indentations is due to the thin primer cup material flowing back into the firing pin recess, and then getting dragged across the holes when the gun is opened. I believe that is what caused your difficulty in opening too.
